Content
Overview
In a virtual experiment a measurement process is modeled mathematically and simulated on a computer. The employed mathematical model of the physical experiment is sought to be as realistic as possible. Virtual experiments allow different scenarios to be easily explored. In this way, measurement processes can be designed and specified with the help of the computer. Virtual experiments can be used to estimate the accuracy that is reached by a real measurement device. Dominant sources of uncertainty can be identified and quantitatively explored by carrying out a sensitivity analysis of the virtual experiment. The results obtained can be used to optimize the considered measurement system. Virtual experiments can help in the development of procedures from data analysis for real experiments, for example to assess and compare different estimation procedures under realistic conditions, or to validate assumptions made about the distribution of measured data.
Research
The research of PTB’s Working Group 8.42 focuses on virtual experiments for optical measurement devices and the development of procedures from data analysis for evaluating corresponding measurements. To this end, the simulation environment SimOptDevice has been developed as a software library, which is successfully employed in many applications regarding length-/form- and coordinate measurements, as well as photometry. SimOptDevice is regularly maintained and its functionality improved. It is currently applied to the tilted-wave interferometer, which is suitable for the optical form measurement of aspheres and freeforms. Methods of data analysis in conjunction with virtual experiments are developed and applied to solve the involved inverse problem and to calibrate the measurement process. Other research topics include the evaluation of uncertainties associated with real measurements utilizing the results of the corresponding virtual experiment, or the use of methods from deep learning in connection with virtual experiments. For example, virtual experiments can be used to create a database needed to train a neural network that is designed for analyzing experimental data.
Publications
Publication single view
Article
| Title: | Reconstructing surface profiles from curvature measurements |
|---|---|
| Author(s): | C. Elster, J. Gerhardt, P. Thomsen-Schmidt, M. Schulz;I. Weingärtner |
| Journal: | Optik - International Journal for Light and Electron Optics |
| Year: | 2002 |
| Volume: | 113 |
| Issue: | 4 |
| Pages: | 154 - 158 |
| DOI: | 10.1078/0030-4026-00138 |
| ISSN: | 0030-4026 |
| Web URL: | http://www.sciencedirect.com/science/article/pii/S0030402604701345 |
| Keywords: | Runge-Kutta method |
| Tags: | 8.42, Form |
| Abstract: | Summary Recently, the measurement of curvature has been suggested as a promising new technique for the highly accurate determination of large-area surface profiles on the nanometer scale. It was shown that the curvature can be measured with highest accuracy and high lateral resolution. However, the reconstruction of surface profiles from curvature data involves the numerical solution of an ordinary differential equation for which initial or boundary values must be specified. This paper investigates the accuracy with which surface profiles can be reconstructed from curvature data. The stability of the reconstructions is examined with respect to the presence of measurement noise and the accuracy of the initial values. The assessment of the reconstruction accuracy is based on an analytical solution (up to numerical integration) derived for the case when the measurement results are given in Cartesian coordinates, and on numerical results in the polar case. The results presented for the latter case allow, in particular, conclusions to be drawn regarding the minimum accuracy of data and initial values required for reconstructing aspheres from curvature measurements with nanometer accuracy. |